Question

The radius of a circle whose area is equal to the sum of the areas of two circles of radii 5 cm and 12 cm is

• A. 13 cm
• B. 14 cm
• C. 15 cm
• D. 17 cm

Answer 1

The correct option is A 13 cm

We know that area of a circle of radius $r=\pi r^2$

By given condition,

$A_3=A_1+A_2$ .....(1)

Since, $r_1=5$ & $r_2=12$

So, by (1), we have

${\pi r}^2={\pi 5}^2+{\pi 12}^2{r}^2=5^2+{12}^{2}r=\sqrt{25+144}=\sqrt{169}=13\text{cm}$